Question
\begin{tabular}{l}\hline\( \equiv \) Listen \\ Factor the expression using the GCF. \\ \( 60-150 x=\square \)\end{tabular}
Ask by Goodwin Gray. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The expression factored using the GCF is \( 30(2 - 5x) \).
Solution
To factor the expression 60 - 150x using the greatest common factor (GCF), first find the largest factor common to both terms.
Step 1: Determine the GCF of the coefficients 60 and 150.
• 60 factors as 2² × 3 × 5
• 150 factors as 2 × 3 × 5²
The common factors are 2, 3, and 5. Therefore, the GCF of 60 and 150 is 2 × 3 × 5 = 30.
Step 2: Factor 30 out of each term:
60 - 150x = 30(2 - 5x)
Thus, the expression factored using the GCF is:
30(2 - 5x)
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Simplify this solution Extra Insights
To factor the expression \( 60 - 150x \) using the greatest common factor (GCF), we first find the GCF of the coefficients 60 and 150. The GCF is 30. Now, we can factor 30 out of the expression: \[ 60 - 150x = 30(2 - 5x) \] Now your expression is factored as \( 30(2 - 5x) \). Nice work—factoring can seem daunting at first, but once you get the hang of finding that GCF, it’s like riding a bike! Exploring other expressions and their factorizations can also be a great way to practice and hone your skills. Keep an eye out for patterns and common factors as you work through more complex mathematical problems!
